Step: 1

Two lines are said to be parallel if they have same slope and different y -intercepts.

Step: 2

The slope intercept form of the equation - 2x + 8y = 10 is y = 1 4 x + 5 4 .

Step: 3

The slope of the line - 2x + 8y = 10 is 1 4 .

Step: 4

So, the slope of the line parallel to - 2x + 8y = 10 is 1 4 .

Correct Answer is : 1 4

Step: 1

[Write the equation of the line.]

Step: 2

Slope of the line is - 1 4 .

[Find the slope of the line using y = m x + b .]

Step: 3

If m is the slope of the line perpendicular to the line y = - 1 4 x + 18 , then

m × - 1 4 = - 1 ⇒ m = 4

Step: 4

Equation | Slope |

- - 4 |

[Find the slope of the line using y = m x + b .]

Step: 5

So, the line y = 4x + 3 7 is perpendicular to the line y = - 1 4 x + 18.

Correct Answer is : y = 4x + 3 7

Step: 1

Slope of the line y = 3x + 4 is 3.

[Compare with y = m x + b .]

Step: 2

Slope of the line y = - 1 3 x + 3 4 is - 1 3 .

[Compare with y = m x + b .]

Step: 3

Product of the slopes of two lines = 3 × (- 1 3 ) = - 1

[Multiply.]

Step: 4

So, the lines y = 3x + 4 and y = - 1 3 x + 3 4 are perpendicular to each other.

[Two lines are perpendicular, if the product of their slopes is - 1.]

Correct Answer is : perpendicular to each other

4

Step: 1

Slope of the line 4x + 5y + 4 = 0 is - 4 5 .

[Slope = - x c o e f y c o e f .]

Step: 2

Slope of the line 5x + 6y + 8 = 0 is - 5 6 .

[Slope = - x c o e f y c o e f .]

Step: 3

Slope of the line 4x + 5y + 6 = 0 is - 4 5 .

[Slope = - x c o e f y c o e f .]

Step: 4

Slope of the line 5x + 9y + 8 = 0 is - 5 9 .

[Slope = - x c o e f y c o e f .]

Step: 5

Lines 4x + 5y + 4 = 0 and 4x + 5y + 6 = 0 are parallel.

[Slopes of parallel lines are equal.]

Correct Answer is : 4x + 5y + 4 = 0 and 4x + 5y + 6 = 0

Step: 1

Slope of y = 2x + 5 is 2.

Step: 2

Slope of ky = (k -1)x + 3k is k - 1 k

[Compare with y = 2x + 5.]

Step: 3

Slopes of two nonvertical lines are equal.

Step: 4

Since the two lines are parallel, so 2 = k - 1 k

Step: 5

2k = k - 1⇒ k = - 1

Correct Answer is : - 1

Step: 1

7x + 13y = - 6

[First equation.]

Step: 2

[Write it in slope-intercept form.]

Step: 3

Hence, the slope is - 7 13 .

Step: 4

[Second equation.]

Step: 5

[Write it in slope-intercept form.]

Step: 6

Hence, the slope is - 1 j .

Step: 7

Since the lines are parallel, - 1 j = - 7 1 3

Step: 8

So, j = 13 7 .

Correct Answer is : 13 7

Step: 1

Two lines are perpendicular, if the product of their slopes is - 1.

Step: 2

For the slopes 4, - 1 4

4 × -1 4 = - 1

4 × -

[Multiply and simplify.]

Step: 3

For the slopes - 4, - 1 4

- 4 × -1 4 = 1

- 4 × -

[Multiply and simplify.]

Step: 4

For the slopes 4, 1 4

4 ×1 4 = 1

4 ×

[Multiply and simplify.]

Step: 5

For the slopes 4, - 4

4 × - 4 = - 16

4 × - 4 = - 16

[Multiply and simplify.]

Step: 6

So, 4 and - 1 4 are the slopes of two perpendicular lines.

Correct Answer is : 4 and - 1 4

Step: 1

Two lines which have the same slope and different y-intercepts are called parallel lines.

Step: 2

Write all the sets of equations in the standard slope-intercept form, y = mx + b and verify.

Step: 3

For the lines x - 3y + 11 = 0, -x + 3y
-7 = 0:

Step: 4

Step: 5

Slope = 1 3 and y-intercept = 11 3 .

[Compare with y = mx + b.]

Step: 6

-x + 3y -7 = 0 ⇒ y = x 3 + 7 3

Step: 7

Slope = 1 3 and y - intercept = 7 3

[Compare with y = mx + b.]

Step: 8

Slopes are same and y -intercepts are different.

Step: 9

So, x - 3y + 11 = 0, -x + 3y -7 = 0 are parallel.

Correct Answer is : x - 3y + 11 = 0, -x + 3y -7 = 0

Step: 1

Two lines which have the same slope and different y-intercepts are called parallel lines.

Step: 2

Write all the sets of equations in the standard slope-intercept form, y = mx + b and verify.

Step: 3

For the lines -x + 5 3 y + 3 = 0, x - 5 3 y - 4 = 0:

Step: 4

-x + 5 3 y + 3 = 0 ⇒ y = 3 5 x - 9/5

Step: 5

Slope = 3 5 and y -intercept = -9 5

[Compare with y = mx + b.]

Step: 6

Step: 7

Slope = 3 5 and y -intercept = - 12 5

[Compare with y = mx + b.]

Step: 8

Slopes are same and y-intercepts are different.

Step: 9

So, -x + 5/3 y + 3 = 0, x - 5/3 y - 4 = 0 are parallel.

Correct Answer is : -x + 5 3 y + 3 = 0, x - 5 3 y - 4 = 0

2

Step: 1

Two lines which have the same slope and different y-intercepts are called parallel lines.

Step: 2

check slopes for all the lines given.

Step: 3

Slope of the line 2x + 5y + 3 = 0 is - 2 5.

[Slope = -x coef/y coef.]

Step: 4

Slope of the line 3x + 4y + 3 = 0 is - 3/4.

[Slope = -x coef/y coef.]

Step: 5

Slope of the line 5x + 4y - 7 = 0 is - 5 4.

[Slope = -x coef/y coef.]

Step: 6

Slope of the line 2x + 5y - 7 = 0 is - 2/5.

[Slope = -x coef/y coef.]

Step: 7

Lines 2x + 5y + 3 = 0 and 2x + 5y - 7 = 0 are parallel.

[Slopes are equal for both the lines.]

Correct Answer is : 2x + 5y + 3 = 0 and 2x + 5y - 7 = 0

Step: 1

3x + 7y + 2 = 0

[First equation.]

Step: 2

[Write it in slope-intercept form.]

Step: 3

Hence, the slope is - 3 7.

Step: 4

7x - ky + 5 = 0

[Second equation.]

Step: 5

[Write it in slope-intercept form.]

Step: 6

Hence, the slope is 7 k
.

Step: 7

Since the lines are perpendicular, (- 3 7 ) × (7 k ) = - 1

[Product of slopes = - 1 for two perpendicular lines.]

Step: 8

So, k = 3.

[Simplify.]

Correct Answer is : 3

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